FROM:Valerie Burke, Chair

TO:Beth Dobkin, Provost

FROM:Valerie Burke, Chair

Academic Senate

DATE:May 20, 2015

RE:Senate Action S-14/15-46CA

Permanent Approval for Math 103

Introduction to Upper Division Mathematics

At the May 13, 2015 meeting of the Academic Senate, the attached Proposal for Permanent Approval for Math 103: Introduction to Upper Division Mathematics was approvedon the Consent Agenda. The proposal wasapproved by a vote of 8-0-0 by the Undergraduate Educational Policies Committee (UEPC) at its April 27, 2015 meeting.All documents related to this proposal can be viewed at the UEPC website (

This action was assigned Senate Action #S-14/15-46CA.

Attachment

cc: President James A. Donahue

Vice ProvostRichard Carp

Dean Roy Wensley

ProposalforPermanentApprovalofMath103

(NB:Math103waspartoftheproposalacceptedinMarch2014toreformthemathematicsmajor.)

1.School:SchoolofScience

Department:DepartmentofMathematicsandComputerScience

CourseNumber:Math 103

CourseTitle:IntroductiontoUpperDivisionMathematics

UpperDivisionStatus:Thiscoursehascollege-levelpre-requisites(seebelow),anden-tailsahighlevelofcognitiveachievement,asitisanin-depthstudyofareasofabstractmathematicsusingthemethodofmathematicalproof.

2.JustificationfortheCourse:Proofsareperhapsthecentralpartofmathematics,astheyaretheformofthelanguagemathematiciansusetocommunicate.Overthepasttwodecadesthemathematicalcommunityhascometorealizethatweneedtobeexplicitinteachingourstudentsaboutthisformandhowtouseit.

Pre-Math103wedidnothaveaclassconcentratingonteachingthetechniquesofproof.StudentslearnedsomeinMath120.Thisknowledgemaybewasbuiltupon,orjustrepeated,inotherupperdivisionmathematicscoursesdependingonthechoicesmadebyindividualinstructorsandthebackgroundsofthestudentsintheclass.Bycreatingaclassinwhichproofsareacentralpillarand having thisclassasthepre-requisitefor severalupperdivisionclasseswewillbeabletocreateamoredevelopmentalmajorinwhichclassescanbuilduponpreviousknowledge.

Inthefuturesomeofourupperdivisioncourseswilltheorybased,andbuildo↵ofthematerialinMath103(thereareMath111,115,131,150,185,193).Ourexpectationisthatthesecourseswillbeabletomovemorequicklyandstudentswillgraspmore,sincetheywillhavehadasemester’sexperiencewithourlanguage.Andotherswillbemoreapplied

coursesandtaughtatalevelreasonableforanystudentwithayearofcalculus(theseareMath113,114,120,134,140).

3.StudentPopulation:Math103is/willberequiredforthemathematicsmajor,andstronglysuggestedforminors.Themathematicsmajor(asrevisedviasubmissiontotheUEPCinMarch2014)hasbeenrevisedsothatthisisnotanadditionalclassforstudents.

4.RelationshiptoPresentCollegeCurriculum:CurrentlyMath120,LinearAlgebraandApplications,isthecoursewherewetrytointroducethetechniqueofproofs.ThisforcesMath120todotoo much.Itistryingtobetheintroductiontoprooftechniquescourseandteachingabstractlinearalgebratothe‘pure’mathmajors,aswellasteachingappliedlinearalgebraandapplicationstothosestudents(sometimesmath,othertimesphysics,economics,etc.)whoareinterestedinthat.MovingtheproofstheorytoMath103willletMath120focus on thetopics ofits title.

Math103willcoveraboutone-halfofthematerialformerlyinMath111.TheremainderofthematerialintheoldMath111andmuchofthatinMath112willbeputintothenewMath111.

Finally,Math103(alongwithMath193)isintendedtoserveasthedepartments“WritingintheDisciplines”class.

5.Anyextraordinaryimplementationcosts:None.Therearenospecialequipmentneedsorunusualclassroomrequirementsassociatedwiththiscourse.

6.LibraryResources:Seeattached.

7.CourseCreditand gradingoptions:Math103isdesignedasalecture/discussioncourse.Studentswhocompletethecoursewillreceiveone(1)SMCcoursecredit. Studentswillmeetwiththeprofessorinclassfor3hours,15minutesperweekthroughoutanacademicsemester.Therewillbeaminimumoftwohoursofstudentworkexpectedoutsideofclassforeveryhourofin-classinstruction.

8.Pre-requisites:(Math27,)Math28or38,andEnglish5.

9.CoursedescriptionworkingforappropriateCollegeCatalog:Thiscourseisanintroductiontomathematicallogicand includes an introduction to Abstract Algebra. Stu-dentswilllearntowriteproofsusingstandard proof-writing organization and terminology.Topicsformalgebrawillincludethedivisionalgorithm,modulararithmeticandgroups.Pre-requisites:English5andMath38,orequivalent.CompletionofMath103andMath193satisfiestheWritingintheDisciplinesrequirementoftheCoreCurriculum.

10.CourseContent: Seeattachedsyllabus

11.ReviewofExperimentalO↵ering:ProfessorSauerbergtaughtMath103inFall2014,basinghissyllabusontheonesubmittedtotheUEPC.Thisistheonlytimethecoursehasbeentaught.HewillalsoteachthecourseinFall2015.

HeadaptedthesyllabusproposedtotheUEPC,butfounditoverlyoptimistic.Afterdis-cussionwiththedepartmentwehavedecidedthatMath103andMath193shouldservejointlyasourWritingintheDisciplinescourses.Thiswillallowtheresearchpaperpartofthecoursetobecovered(asitalreadyis)inMath193.HisFall2015syllabusandschedulewillbesimilartotheonesubmittedwiththisproposal.

Theremainingmaterialinthecourseworkswell,andasanintensive,andwritingintensivecourse,thisshouldbeasuccessfulcourse.

ReviewofLibraryResourcesandInformationLiteracyForMATH103:IntroductiontoUpperDivisionMathematicsLindaWobbe,April2015

MATH103isrequiredofallmathematicsmajorsandminorsasanintroductiontoformalproofsandhigh-levelmathematicstopicsincludingAbstractAlgebra. Thewritingassignmentinvolvesthecreationoflogicalmathematicalproofs.Studentswillbeexpectedtoachieveadeeplevelofunderstandinginawidevarietyofmathematicalconcepts,andwillbenefitfromresourcesthatofferexplanationsandexamplesdifferentfromtherequiredtexts.

I.RequiredResources. TheLibrarywillobtaintherequiredtextsforthisclass,fortextbookreserve.

II.ReferenceSources. Referencesourcesprovidebasicexplanationsanddefinitions,andmaybehelpfultostudentsinthesecourses. TheLibrary’sSubjectGuideforMathematicsliststhefollowingreferencedatabasesCredoLiteratiAccessScience,andthefollowingindividualtexts:

PrincetonCompaniontoMathematics.(Ref510G747pandonline)

WordsofMathematics:anEtymologicalDictionaryofMathematicalTermsUsedinEnglish.(ebrary eBook)

CRCconciseencyclopediaofmathematics(Ref 510.3W438)

Companionencyclopediaofthehistoryandphilosophyofthemathematicalsciences(Ref

510.9G773c)2vols.

Encyclopedicdictionaryofmathematics(Ref510.3It6)4vols.

TheVNRconciseencyclopediaofmathematics(Ref 510.2G282)

III.Books.Mathematicsingeneralismorebook-dependentthanotherdisciplinesintheSchoolofScience. Themathematicsfacultyareresponsiveandengagedinselectingthebestofthenewmathematicspublications. TheLibrary’scollectionincludesabout5,000mathematicstexts,withapproximately$5,000peryearspenttomaintainthemathematicsbookcollection. Thiscourseexploresmanytopics,includingsets(87),induction(20),modulararithmetic(20),abstractalgebra,proofs(95)andgroups(122).ThenumberoftextsintheLibrarycollectionfollowseachterm.

ExamplesofbooksintheLibrarycollectionthatsupportthiscourseinclude: Extendingthefrontiersofmathematics:inquiriesintoproofandargumentation(511.3B865)

Distillingideas:anintroductiontomathematicalthinking(510K159)

Abstractalgebraandsolutionbyradicals(512.02M450)

Therealnumbers:anintroductiontosettheoryandanalysis(511.322St54r)

Aninvitationtoabstractmathematics(510B167)

Roadstoinfinity:themathematicsoftruthandproof(511.322St54)

Proofinmathematicseducation:research,learningandteaching(511.3R272)

Proofiness:thedarkartsofmathematicaldeception(510Se42)

Truththroughproof:aformalistfoundationformathematics(510.1W433)

Charmingproofs:ajourneyintoelegantmathematics(511.3AL78)

IV.Journals. TheLibrary’scollectionalsoincludesover500mathematicsjournalsandthekeydatabaseforarticlediscovery,MathSciNet. JSTOR’sMathematicsandStatisticspackageofjournalarchivesissubscribed. Thecostofsubscribingtothesejournalsanddatabasesisabout$12,000annually.Articlesinmanymathematicsjournalsarehighlyspecialized,andbeyondthereachofundergraduatestudents. Tohelpdirectstudentstothecoreandmostaccessiblemathematicsjournals,theLibraryMathematicsSubjectGuidepresentsabrowsingcollectionwhichcaneachbesearchedindividually,including:

AmericanMathematicalMonthly

TheBulletinandtheNoticesoftheAmericanMathematicalSocietyMathematical Intelligencer

UMAPJournal

IV.LibrarianRecommendations.ThetextbooksforthecourseareonorderfortheLibrary’stextbookcollection. Ongoingcommunicationwiththemathematicsfacultyisexpected tocontinue,andwillensuretheLibrary’scollectionissufficienttomeetthe needsofstudentsinthiscourse. TheSubjectSelectorLibrarianishappytoseethesyllabusadvertisingtheavailabilityof individualstudentappointmentswiththelibrarian.ClassroompresentationscanalsobemadeavailablebythelibrariantoguidestudentstothewealthofresourcesofferedbytheLibrary’scollection.

Math103:IntroductiontoUpperDivisionMathematicsSaintMary’sCollege

Fall2014

Professor:JimSauerberg

Office:GalileoHall101A.Phone:631-4248.e-mail:

webpage:Onmath.stmarys-ca.edu

Lecture:MWF8:00–9:05amGaraventa120.

Coursewebpage:OnMoodle

OfficeHours:Officehourswillbepostedonmyofficedoor(generallyincludingMF9:30am

–12:00pmandT11:30am–2:00pm).Officehoursarethebestplacetogetyourquestionsaboutcoursecontentandhomeworkanswered.

Text:Reading,Writing,andProving.ACloserLookatMathematicsbyUlrichDaeppandPamelaGorkin.AndABookofAbstractAlgebrabyCharlesC.Pinter.Botharerequired.Makesuretogetthe2ndeditionofeach.

Prerequisites:English5andMathematics38,orequivalent.

Major,MinorandCoreCurriculum:Math103isrequiredforalltracksofthemathe-maticsmajor,andisalsoarequiredpartofthemathminor.CompletionofMath103andMath193satisfiestheWritingintheDisciplinesrequirementoftheCoreCurriculum.

CatalogCourseDescription:“ThiscourseisanintroductiontomathematicallogicandproofsandincludesanintroductiontoAbstractAlgebra. Studentswilllearntowriteproofsusingstandardproof-writingorganizationandterminology.Topicsfromalgebrawillincludethedivisionalgorithm,modulararithmetic,ringsandgroups.”

CourseObjective:Thecentralpurposeofthiscourseistoteachyouthecarefuluseoflanguageinthecontextofmathematicalreasoningandproof.Mostofyourcoursessofarhaveconcentratedonlearningalgorithmsforsolvingparticulartypesofproblems;mostcoursesafterthisonewillfocusonlogicalreasoning,conceptualunderstanding,andproofs.Thiscourseisthe“bridge”betweenthetwowaysofapproachingmathematics.Indeed,afterintroductingformal,rigorousmathematicswhichemphasizeslogicandaxiomaticthinking,andlearningvariousstandardtechniquesofproof,wewillapplythislearningtoseveralareasofmathematics.

Grading:Gradesmeasureperformance,notdesireorworkethicorpersonalityortimespentoranyotherquality.Thus,preparationisessentialanddemonstrationiscrucial.

300ptsHomework,Quizzes,Participation200ptsMidtermExams(100ptseach)200ptsFinalExam

CourseGoals:Thiscourseisanintroductiontomathematicallogicandproofwriting.Studentswillbecomeproficientat:

•Recognizingandcomposingbasiclogicstatements,includingthebooleanoperatorsandquantifiers.

•Recognizingandcomposingstatementsofimplication,conversestatements,contrapos-itivestatements,andnegationsofstatements.

•Explainingthedi↵erencebetweenAxioms,Definitions,Lemmas,Theorems,andCorol-laries.

•Readingproofs,understandingtheassumptionsmadeintheproof,andfollowingtheclearandcarefulorganizationofwell-constructedstatementsofimplicationsleadingtoalogicalconclusion.

•Writingproofsusingstandardproof-writingorganizationandterminology,makingtheassumptionsclearandusingcarefulorganizationofwell-constructedstatementsofimplicationstoleadtoalogicalconclusion.

•Techniquesofproof-writing,includingthetechniquesofdirectproof,proofbycontra-diction,andinduction.

•Analyzingargumentssoastoconstructonesthatarewellsupported,arewellreasoned,andarecontrolledbywell-definedaxiomsand/orassumptions.

•Usingtheprocessofpre-proof-writingandscratchworktoenhanceintellectualdiscoveryandunravelcomplexitiesofthought.

Youwillalsopracticeyournewproofreadingandproofwritingskillsintheareasof

•Setsandtheiroperations

•Divisors,thedivisionalgorithm,andEuclid’sAgorithm

•MathematicalInduction

•InjectiveandSurjectiveFunctions

•ModularArithmeticandLinearCongruences

•Groupsandtheirsubgroups

AttendanceandParticipation:Youareexpectedtoattendandparticipateineveryclasssession.Timeintheclassroomwillbespentonlecture,small-groupdiscussions,shortpresentationsby students, andlargerinteractivediscussionasanentireclass.Ifyoumissclass youwillmisstheseopportunitiestolearnandpracticeskillsthatcontributetoyourdevelopmentasamathematicalthinker.Youmayalsomissaquizandtherearenomake-ups.Finally,ifyoumissnumerousclasses,Iwillthinkthatyouarenotseriousaboutyoureducationandwillrememberthatwhenassigningyourgradeattheendofthesemester.

Homework:Homeworkisthemostimportantpartofthisclass.Youshouldworkoftenandassiduouslyonit,rereadingandrevisingyoursolutionsuntiltheyarecorrect,concise,efficient,andelegant.Suche↵ortsarethebestway(theonlyway?)todeepenyourunder-standingofthematerial.Don’tthinkofhomeworkasproblemsthathaveanswersbutasessaypromptswithresponsesthatcan(almost)alwaysbepolishedandimproved.

Homeworkwillbe“sca↵olded”inthatyouwillbuildcontinuallyuponpreviouslylearnedskills.Afteryoulearntowritelogicstatementsandimplicationstatements,youwilllearntousequantifiersandtowritenegationsofthesemorecomplicatedimplicationstatements.Thisbasicmathematicalgrammarwillbeusedwhenyoulearntowriteproofsofyour

implicationstatements.YouwillthenpracticethesewritingandprovingskillsintheareasofSetTheory,ElementaryNumberTheory,andAbstractAlgebra.Proofwritingisthecoreofmathematics(andofthisclass).Inordertomasterproof-writing,youmustreadandwritemanyproofs.Homeworkwillwherethiswillhappen.

Itisunderstoodthatyouronlysourcesofinformationforthehomeworkwillbeourtexts,anynotesyoutookinorforclass,yourclassmates(whenpermissible),yourprofessorandyourbrainpower.

Latehomeworkwillnotbeacceptedforanyreason.

WrittenAssignments:Becauseinmanywaysthisisalanguagecourse,youwillbeex-pectedtolearntoclearlyandpreciselyexpressmathematicalideasinwriting.Inadditiontoconsideringitsmathematicalcontent,thegradingofyourworkwilltakeintoconsider-ationclarityofexpression,completeness,properusageofbothEnglishandmathematicalgrammar,andwhetheryoureallysaidwhatyoumeanttosay. Theproblemswillbegradedonascaleof1to5.Youshouldnotthinkofthegradeasrepresentingapercentagebutasdeliveringamessage:

5—excellentwork;norealcomplaintsoncontentoronwriting.

4—argumentbasicallycorrectbutmissingsomeminordetailsorcontainingsmallerror(s).3—argumentmostlycorrect,butcontainssignificantmisstepinthemathematics; or,anespeciallypoorlywrittenproof.

2—seriousgapsinthemathematics.

1—someideasintherightdirection,butdidn’treallygetthere.0—didn’tdotheproblemoritwascompletelywrong.

Whenyouwriteupanassignment,youareexpectedtoincludesufficientlymanydetailstoenlightensomeonewhodoesnotalreadyknowwhatyouaretryingtosay. Thismayrequirethatyourestateadefinitionorprevioustheoremandsayhowitisusedinyourproof.Donotbeafraidtoincludetoomanydetails.

Quizzes:Daysmaybeginwithashortquizonrecentmaterial.(Thiswillalmostalwaysbedefinitionsandquickcomputations.)Absolutelynolatequizzeswillbegiven.

Take-homeexams:Homeworkwillregularlyincludequestionsthatyouaretosolvebyyourself.Thesearemeanttoprovidebothyouandmewithanindicationofyourpersonal

progressintheclass.Asopposedtotheotherpartsofthehomework,youareonyourhonornottodiscussthesequestionswithanyonebutProfessorSauerberg.Youarefreetouseanyclassnotes,anypreviouslyprovedtheorems,andanythingthatisdistributedinclass.However,youmaynotconsultanybooksexceptthetextbooks,noranyoutsidesources,includingon-linesources.

CultureofCooperationandPlagiarism:Youareexpectedtoworkcooperatively,aswellastotakeresponsibilityforyourownlearning.

Whatyoushoulddo:Discussideasandaskeachother(andme)forhelp.Giveandaskforconstructiveinput,praisingandcriticizingwhereappropriate.Individuallydigestallideasandindividuallywriteyourproofs/solutions.Noteoneachproblemwho(ifanyone)youworkedwith.Rememberthatonthequizzesandtheexamsyouareonyourown,soyouneedtofullyunderstandeachsolution.Insummary,keepcollaborationconstructiveandreasonable.

BeclearthatAnymaterialyousubmitmustbeyourownwork.Itisanactofplagiarismtocopy,inanyway,allorpartofanysolutionwithoutacknowledgment.Itisalsoanactofplagiarismtopermitanothertocopyinanywayallorpartofoneofyoursolutions.Ifyouusesomeoneelse’sideasinyoursolution(oranyotherworkthatyoudoanywhere), youmustgivecredittothatperson,andbesurethatyouunderstandthatworkaswellasifitwere your own.SeetheStudentHandbokforspecificdetails.

In-classexams:Thepurposeofexamsistoencouragethedevelopmentofthenextlevelofproficiencyofthecoursematerial.Thequestionswillgenerallybestraightforwardforanyonewhohasbeendigestingthematerialalongtheway.Typicalquestionswillaskyoutodefineimportantterms,answerandexplaintrue/false,giveashortanswertoquestionsonthematerial,stateanimportanttheorem,developandgivesimpleproofs.

Therewillbetwoin-class,closed-bookexams,likelyMondaySeptember29thand

WednesdayOctober29th.ThefinalexamwillbeMondayDecember8that8:00am.

Theonlyacceptablereasonformissinganexamisasuddenunexpectedseverepersonalemergency.A0willresultfrom an unexcusedabsence.Makeupexamswillnotbegivenforillness,brokenalarmclock,flattire,roommatefromhell,badmysterymeat,etc.

GradingPolicy:

A.Collegedefinition: Excellent

Math103: Outstandingachievement;availableonlyforthehighestaccomplishment.Youarethoroughlyfamiliarwithalldefinitionsandexamplescovered,canpreciselystateandcorrectlyprovealmostallassignedtheoremsfromclass,candoallofthehomeworkexercises,andcanusetheconceptsyoulearnedinthiscoursetosolveunfamiliarproblemscomparableincomplexitytothosedoneinclassandonthehomework.

B.Collegedefinition:Verygood

Math103:Praiseworthyperformance;definitelyaboveaverage.

Youarethoroughlyfamiliarwithalldefinitionsandexamplescovered,canpreciselystateandcorrectlyprovemosttheoremsfromclass,candomostofthehomeworkexercises,andcanusetheconceptsyoulearnedinthiscoursetosolvemostunfamiliarproblemsofcomparablecomplexity.

C.Collegedefinition:Satisfactory Math103:Satisfactoryperformance.

Youarefamiliarwithalldefinitionsandmostexamplescovered,canstateandprovewithoutmajormistakesmanytheoremsfromclass,candothemajorityofthehomeworkexercises,andcanusetheconceptsyoulearnedinthiscoursetosolvesomeunfamiliarproblemsofcomparablecomplexity.

D.Collegedefinition:Barelypassing

Math103:Minimallypassing;lessthanthetypicalundergraduateachievement.

Youarefamiliarwiththemajorityofdefinitionsandmanyexamplescovered,canstateandproveatleasthalfofthetheoremsfromclass,candoatleasthalfofthehomeworkexercises,andcanusetheconceptsyoulearnedinthiscoursetosolveatleastafewunfamiliarproblemsofcomparablecomplexity.

E.Collegedefinition:Failing.

Math103: Youhavedifficultystatingdefinitionsandcomingupwithexamples,donotrememberstatementsoftheoremsand/orcannotprovethem,candofewofthehomeworkexercises,andlacktheskillstoattachunfamiliarproblemsofcomparablecomplexity.

Centerfor WritingAcrosstheCurriculum(CWAC)writing-across-the-curriculumo↵erstwo options for all students, of all disciplines and levels:WritingCircles: Studentsregisterforthe.25courseCOMM190:WritingCirclesandthencontactCWACtoselectaweeklyCircletime.Studentssignup before orduringthefirstweekofthesemester.Duringthesmall-groupworkshops,writersdiscusstheirownprojects,atallstagesoftheprocess.

One-on-onesessions:Studentscall925.631.4684tomakeappointmentsordropin,Dante

202.OnlinesessionsviaSkypeareavailable.Fallhours:4–8p.m.Sunday;12–8p.m.Monday;12–6p.m.Tuesday;and12–8p.m.WednesdayandThursday.WritingAdvisersguidetheirpeerstowardexpressingideasclearly,alwaysweighingaudienceandpurpose.Writersbringtheirassignmentsheetsandreadingsinordertobrainstormideas,revisedrafts,orworkonspecificaspectsofwriting,suchasgrammar,citation,thesisdevelopment,organization,criticalreading,orresearchmethods.Theymaydiscussanygenre,includingpoetry,sciencelabreports,argument-drivenresearch,orscholarshipapplicationletters.

LibraryResources:Reference/InformationassistanceisavailableattheReferenceDesk,byphone(925)631-4624,textmessageat(925)235-4624orChat(IM). ChecktheLibrarys“AskUs”linkfordetails:r(925)631-4232.

Math103,Fall2014,TentativeSchedule

DATE / TEXT / TOPIC(S)
Wed.Sept.3 / Chapter1 / Introduction
Fri.Sept.5 / Chapter2 / IntroductiontoLogicalConstructions
Mon.Sept.8 / Chapter3 / ContrapositiveandConverse
Wed.Sept.10 / Chapter4 / SetNotationandQuantifiers
Fri.Sept.12 / Chapter5 / Proof Techniques
Mon.Sept.15 / Chapter6 / Sets
Wed.Sept.17 / Chapter6 / ProofwithSets
Fri.Sept.19
Mon.Sept.22 / Chapter7 / LATEX
OperationsonSets
Wed.Sept.24 / Chapter9 / PowerSet
Fri.Sept.26 / extra
Mon.Sept. / 29 / EXAM1
Wed.Oct.1 / Chapter18 / Induction
Fri.Oct.3 / Chapter18 / Induction
Mon.Oct.6 / DivisorsandDivisionAlgorithm
Wed.Oct.8 / Euclid’sAlgorithm
Fri.Oct.10 / Congruences
Mon.Oct.13 / LinearCongruences,Zn
Wed.Oct.15 / Chapter14 / Functions
Fri.Oct.17 / Chapter15 / InjectiveandSurjective
Mon.Oct.20 / Chapter16 / Inverses
Wed.Oct.22 / Fermat’sTheorem
Fri.Oct.24 / NoClass
Mon.Oct.27 / Chapter2P / Operations
Wed.Oct.29EXAM2
Fri. / Oct.3 / Chapter3P / Groups
Mon. / Nov.3 / Chapter3P / MoreExamples
Wed. / Nov.5 / Chapter4P / ElementaryProperties
Fri. / Nov.7 / Chapter5P / Subgroups
Mon. / Nov.10 / Chapter5P / Subgroups
Wed. / Nov.12 / Chapter10P / Orderofelement
Fri. / Nov.14 / Chapter11P / CyclicGroups
Mon. / Nov.17 / Chapter11P / CyclicGroups
Wed. / Nov19 / Chapter13P / CountingCoset
Fri. / Nov.21 / Chapter13P / Lagrange’s Theorem
Mon. / Nov.24 / Chapter13P / Consequences
Wed. / Nov.26 / NoClass
Fri. / Nov.28 / NoClass
Mon. / Dec.1 / Chapter14P / Homomorphism, Kernals
Wed. / Dec.3 / Chapter14P / Isomorphisms
Fri. / Dec.5 / extra

Mon.Dec.8FINALEXAM